Villa came into Friday's game having won their first four games of a league campaign for the first time since 1930-31, but three expert finishes from the Leeds striker prevented the hosts making it a club record five victories on the spin to open their season.
The result lifts Leeds to third - their highest position at the end of a day in the division since September 2002.
It was reward for a relentlessly positive performance from an injury-hit visiting side that should probably have yielded more goals.
Leeds boss Marcelo Bielsa later stated: "It was a good performance, it was better in the second half. The first half was also good, we defended well, we attacked well and we had the luck to score before they did."
On Patrick Bamford's hat-trick, he also said: "I'm very happy for him, they were all very nice goals. Some of the nicest goals he has scored for us.
"I think his development is more to do with him and less to do with me."